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3 years ago

Find the area of the shaded region

Mathematics

1 answer:

AlexFokin [52]3 years ago

5 0

Answer:

7 $\pi$ cm²

Step-by-step explanation:

First, find the area of the big circle with the formula A = $\pi$ r²

A = $\pi$ (3)²

A = 9 $\pi$

Now, we can find the areas of the smaller circles. Since they have the same radius, they are congruent (will have the same area)

A = $\pi$ r²

A = $\pi$ (1)²

A = $\pi$

Now, we will subtract the areas of the smaller circles from the area of the big circle to find the area of the shaded region:

9 $\pi$ - $\pi$ - $\pi$ = 7 $\pi$

So, the area of the shaded region is 7 $\pi$ cm²

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4 years ago

What is the period of the function f(x)=sin(x/2)

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3 years ago

HELP ASAP HELP PLEASE ASAP

Gnesinka [82]

Answer:

WXYZ can not be a rectangle because consecutive sides are not perpendicular to each other.

Step-by-step explanation:

The given vertices are W(-4,3), X(1,5), Y(3,1) and Z(-2,-1).

Plot these points on coordinate plane and draw the quadrilateral as shown below.

$Slope=\dfrac{y_2-y_1}{x_2-x_1}$

Using this formula, we get

$m_{WX}=\dfrac{5-3}{1-(-4)}=\dfrac{2}{5}$

$m_{XY}=\dfrac{1-5}{3-1}=\dfrac{-4}{2}=-2$

Now,

$m_{WX}\times =\dfrac{2}{5}\times (-2)=-\dfrac{4}{5}\neq -1$

Here, WX and XY are two consecutive sides of quadrilateral but the product of their slopes is not equal to -1. It means they are not perpendicular to each other.

Since, all interior angles of a rectangle are right angles, therefore, WXYZ can not be a rectangle.

5 0

3 years ago

Choose a system of equations with the same solution as the following system:

Lina20 [59]

Answer:

Option A.

Step-by-step explanation:

We are given 6x+2y =-6 ......(1) and 3x-4y=-18 .....(2)

Solving equations (1) and (2) we get

12x+3x =-30, ⇒x= -2 and from equation (1), 2y= -6-6(-2) =6, ⇒ y=3

Therefore, the solution for the given set of equations is x= -2 and y=3

A) Solving the equations 8x+4y = -4 ....... (3)and 17x+2y =-28, we get

8x -34x = -4 -(-56) =52, ⇒-26x =52, ⇒x=-2 and from equation )(3), we get -16+4y =-4, ⇒ y=3

Therefore, the solution x=-2 and y =3 match with the original solution.

B)Solving the equations 12x + 4y = 12 ....... (4)and 21x + 2y = −36, we get

12x -42x = 12 -(-72) =84, ⇒-30x =84, ⇒x=-84/30.

Therefore, the solution x=-84/30 does not match with the original solution.

C) Solving the equations 6x + 8y = −36 ....... (4) and 15x + 6y = −60, we get 18x -60x = -108 -(-240) =132, ⇒-42x =132, ⇒x=-132/42

Therefore, the solution x=--3 do not match with the original solution.

D) Solving the equations 6x + y = 15 ....... (5) and 15x − y = −9, we get 6x +15x = 6, ⇒21x =6, ⇒x=2/7

Therefore, the solution x=2/7 do not match with the original solution.

Therefore, option A) will have the same solution. (Answer)

4 0

3 years ago

In rectangle JKLM, JK is equal to 10 feet and MN is equal to 25 feet, find JL.

Snezhnost [94]

we know that

if JKLM is a rectangle

then

diagonals

MK=JL

MK=2*MN------> MK=2*25 ft------> MK=50 ft

JL=MK----> JL=50 ft

therefore

the answer is

JL is 50 ft

7 0

4 years ago